Note that while the appearance kernel in Equation (REF ) is invariant to global similarity transforms due to descriptor invariance, the geometry kernel in Equation (REF ) measures zero-mean keypoint displacement and thus requires data to be aligned within a common spatial reference frame. Alignment may be established via standard subject-to-atlas registration prior to keypoint extraction or from keypoint correspondences after extraction using feature-based alignment [1]}. The following workflow is used to compute pairwise distances for a set of \(N\)  images:
